Keywords
- Vector Field
- Hopf Bifurcation
- Phase Portrait
- Double Root
- Transcritical Bifurcation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, “Theory of Bifurcations of Dynamic Systems on a Plane,” Israel Program for Scientific Translations, John Wiley & Sons, New York, 1973.
A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, “Qualitative Theory of Second-Order Dynamic Systems,” Israel Program for Scientific Translations, John Wiley & Sons, New York, 1973.
C. Chicone and D. S. Shafer, Separatrix and limit cycles of quadratic systems and a theorem of Dulac, Trans. Amer. Math. Soc. 278 (1983), 585–612.
H. I. Freedman, “Deterministic Mathematical Models in Population Ecology,” Marcel Dekker, New York, 1980.
J. Guckenheimer and P. Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields,” Springer-Verlag, New York, 1983.
N. Kopell and I. N. Howard, Bifurcations and trajectories joining critical points, Adv. in Math. 18 (1975), 306–358.
J. E. Marsden and M. McCracken, “The Hopf Bifurcation and Its Applications,” Springer-Verlag, New York, 1976.
H. I. Freedman and G. S. K. Wolkowocz, Predator-Prey systems with group defence: the paradox of enrichment revisited, Bull. Math. Biol. 48 (1986), 493–508. [not cited].
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Rothe, F., Shafer, D.S. (1990). Bifurcation in a quartic polynomial system arising in biology. In: Françoise, JP., Roussarie, R. (eds) Bifurcations of Planar Vector Fields. Lecture Notes in Mathematics, vol 1455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085400
Download citation
DOI: https://doi.org/10.1007/BFb0085400
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53509-6
Online ISBN: 978-3-540-46722-9
eBook Packages: Springer Book Archive
